In a recent work (Mosyak, A.; et al. J. Chem. Phys. 1996, 104, 1549), we investigated numerically electron tunneling through water layers confined between two solid walls. In the present paper, the effect of some of our model assumptions and parameters on the tunneling behavior is studied. In particular, we focus on the role played by the water electronic polarizability. We find that the tunneling behavior computed with water configurations prepared with a polarizable SPC water model is very similar to that obtained with configurations prepared using the nonpolarizable RWK2-M water model used previously, provided that the same electron-water pseudopotential is invoked. On the other hand, including the self-consistent many-body potential associated with the water electronic polarizability in the model for the electron-water interaction has a profound effect on the tunneling behavior, making the tunneling probability similar to 2 orders of magnitude larger than calculated with the nonpolarizable model. This rectifies the disagreement found before between the tunneling behavior computed with the nonpolarizable water model and experimental results. The strong effect of including the many-body polarizability interactions found in the present study stands in marked contrast to the relatively weak effect found in the context of electron hydration and hydrated electron spectroscopy. The origin of this effect is traced to properties of the lowest excess electron states found for neutral water configurations in the two models: The states associated with the polarizable model are of lower energy yet more extended than the corresponding levels found for the nonpolarizable model. We suggest that the existence of these lower, more extended electronic states in the polarizable model plays a decisive role in the observed lower effective barrier to tunneling through water as compared with vacuum.